304 H. S. WILLIAMS PERSISTENCE OF FLUCTUATING VARIATIONS 



value of the three ratio indexes, without attempting to interpret them 

 into characters, in estimating the following results. 



RESULTS 



Explanation of the ratio indexes. — The chief results are expressed in 

 the mathematical values of the three ratio indexes E\ R-, W : 



R^ stands for the form of the shell ; 



R2 stands for the proportionate size of the muscular scar in relation to 

 the size of the pedicle valve; 



R^ stands for the form of the pedicle muscular scar. 



The index L stands for size of shell expressed in millimeters ; 



L^ stands for size of the muscular scar in millimeters. 



1. Size of shells — Values of index L. — {a) The average length of 277 

 specimens from all zones is 19.1 millimeters. 



(b) The mean of averages for the 35 separate faunules is 19.8 milli- 

 meters. 



(c) Average length of the separate specimens of each zone by zones is, 

 for 20 Hamilton specimens, 18.2 millimeters; for 24 Ithaca specimens, 

 17.5 millimeters; for 115 Van Etten specimens, 18.6 millimeters; for 40 

 Owego specimens, 20 millimeters; for 78 Swartwood specimens, 19.8 

 millimeters. 



Uniformity in average size. — {d) This shows a remarkable uniformity 

 in the aA^erage size of the specimens; the value of L varies from 17.5 to 

 20 — ^that is, 2% millimeters. 



Here it should be noted that special directions were given to the col- 

 lectors to make no selection in collecting specimens, but to gather speci- 

 mens as far as practicable to represent the actual relation of abundance 

 and rarity shown by the several species and the range in variation in size 

 and other characters expressed by each species for each separate faunule. 



Length of shell increases on passing upward. — (e) Examination of 

 result (c) above shows that there is a slight increase in the average size 

 of the shell on pasing upward. This is in harmony with another fact not 

 brought out by the statistics. The thickness of the shells shows a decided 

 increase on passing upward. In the Hamilton and Ithaca zones the shells 

 are mainly frail and often crushed in fossilization. In the upper zones 

 rarely are any specimens crushed, and there are frequent specimens show- 

 ing thickening at the margin and strengthening of the processes about the 

 hinge and bordering the muscular scars. 



Size alone not significant of evolution. — (/) The size of the shell 

 alone, however, can not be used as an index of evolution, because each 



) 



